There is a set of tiles which are all different and coloured just on the edges. Each edge on a tile is a different colour. For example: |

Altogether $10$ different colours are used for the edges, and there is an equal number of edges of each colour used throughout the set. |

The whole set of tiles is used to make a
square. This has a green and blue border. There are no green or
blue tiles anywhere in the square except on this border. |

How many tiles are there in the set? |